An exact mapping from ReLU networks to spiking neural networks.

Deep spiking neural networks (SNNs) offer the promise of low-power artificial intelligence. However, training deep SNNs from scratch or converting deep artificial neural networks to SNNs without loss of performance has been a challenge. Here we propose an exact mapping from a network with Rectified Linear Units (ReLUs) to an SNN that fires exactly one spike per neuron. For our constructive proof, we assume that an arbitrary multi-layer ReLU network with or without convolutional layers, batch normalization and max pooling layers was trained to high performance on some training set. Furthermore, we assume that we have access to a representative example of input data used during training and to the exact parameters (weights and biases) of the trained ReLU network. The mapping from deep ReLU networks to SNNs causes zero percent drop in accuracy on CIFAR10, CIFAR100 and the ImageNet-like data sets Places365 and PASS. More generally our work shows that an arbitrary deep ReLU network can be replaced by an energy-efficient single-spike neural network without any loss of performance.

Proton leap: shuttling of protons onto benzonitrile.

The detailed description of chemical transformations in the interstellar medium allows deciphering the origin of a number of small and medium - sized organic molecules. We present density functional theory analysis of proton transfer from the trihydrogen cation and the ethenium cation to benzonitrile, a recently discovered species in the Taurus Molecular Cloud 1. Detailed energy transformations along the reaction paths were analyzed using the interacting quantum atoms methodology, which elucidated how the proton carrier influences the lightness to deliver the proton to benzonitrile's nitrogen atom. The proton carriers' deformation energy represents the largest destabilizing effect, whereas a proton's promotion energy, the benzonitrile-proton Coulomb attraction, as well as non-classical benzonitrile-proton and carrier-proton interaction are the dominant stabilizing energy components. As two ion-molecule reactions proceed without energy barriers, rate constants were estimated using the classical capture theory and were found to be an order of magnitude larger for the reaction with the trihydrogen cation compared to that with the ethenium cation (∼10-8 and 10-9 cm3 s-1, respectively). These results were obtained both with quantum chemical and ab initio molecular dynamics simulations (the latter performed at 10 K and 100 K), confirming that up to 100 K both systems choose energetically undemanding routes by tracking the corresponding minimum energy paths. A concept of a turning point is introduced, which is an equivalent to the transition state in barrierless reactions.

The significance of the metal cation in guanine-quartet - metalloporphyrin complexes.

The planarity and the appropriate size of the porphyrin ring make porphyrin derivatives ideal ligands for stacking to guanine quartets and they could thus be used as anti-cancer drugs. In this contribution we analyzed complexes of a guanine quartet with a porphyrin molecule, magnesium porphyrin and calcium porphyrin. As magnesium and calcium ions are located in the center and above the porphyrin ring, respectively, the two metalloporphyrins are expected to have different impacts on the target. The optimized structures of the three systems revealed geometrical changes in the guanine quartet upon complexation: while stacking of porphyrin and magnesium porphyrin does not induce significant changes, calcium porphyrin considerably distorts the quartet's structure, which has significant implications for the binding properties among guanine molecules. Ab initio molecular dynamics simulations revealed that the systems perform small fluctuations around the equilibrium structures. The largest atom displacements are performed by the calcium ion. The interacting quantum atoms methodology enabled analysis of the binding properties in the studied complexes. Interestingly, although the proximity of the calcium ion is responsible for the quartet's pronounced deformation and weakening of guanine-guanine binding, it also enables stronger binding of the metal ion to the quartet, resulting in a more stable complex. These results imply that metalloporphyrin-like ligands with out-of-plane central ions might represent promising drug candidates in anti-tumor treatment.

Intriguing Intermolecular Interplay in Guanine Quartet Complexes with Alkali and Alkaline Earth Cations.

The possibility to target noncanonical guanine structures with specific ligands for therapeutic purposes inspired numerous theoretical and experimental investigations of a guanine quartet and its stacked composites. In this work, we employed the interacting quantum atoms methodology to study interactions among different fragments in complexes composed of a guanine quartet and alkali (Li+, Na+, K+) or alkaline earth (Be2+, Mg2+, Ca2+) cations in vacuo: metal-quartet interaction, influence of the cation on guanine-guanine interaction, as well as hydrogen bond cooperativity in the guanine quartet and its complexes with metal ions. Interestingly, although the presence of a cation intensifies interaction among guanine molecules, it lowers their binding energy because of notable quartet's distortion which is responsible for guanines' substantial deformation energy. This phenomenon is particularly pronounced with Be2+ which, out of the six analyzed cations, enhances hydrogen bond cooperativity to the greatest extent.

Corticosterone oscillations during mania induction in the lateral hypothalamic kindled rat-Experimental observations and mathematical modeling.

Changes in the hypothalamic-pituitary-adrenal (HPA) axis activity constitute a key component of bipolar mania, but the extent and nature of these alterations are not fully understood. We use here the lateral hypothalamic-kindled (LHK) rat model to deliberately induce an acute manic-like episode and measure serum corticosterone concentrations to assess changes in HPA axis activity. A mathematical model is developed to succinctly describe the entwined biochemical transformations that underlay the HPA axis and emulate by numerical simulations the considerable increase in serum corticosterone concentration induced by LHK. Synergistic combination of the LHK rat model and dynamical systems theory allows us to quantitatively characterize changes in HPA axis activity under controlled induction of acute manic-like states and provides a framework to study in silico how the dynamic integration of neurochemical transformations underlying the HPA axis is disrupted in these states.

The HPA axis and ethanol: a synthesis of mathematical modelling and experimental observations.

Stress and alcohol use are interrelated-stress contributes to the initiation and upholding of alcohol use and alcohol use alters the way we perceive and respond to stress. Intricate mechanisms through which ethanol alters the organism's response to stress remain elusive. We have developed a stoichiometric network model to succinctly describe neurochemical transformations underlying the stress response axis and use numerical simulations to model ethanol effects on complex daily changes of blood levels of cholesterol, 6 peptide and 8 steroid hormones. Modelling suggests that ethanol alters the dynamical regulation of hypothalamic-pituitary-adrenal (HPA) axis activity by affecting the amplitude of ultradian oscillations of HPA axis hormones, which defines the threshold with respect to which the response to stress is being set. These effects are complex-low/moderate acute ethanol challenge (<8 mM) may reduce, leave unaltered or increase the amplitude of ultradian cortisol (CORT) oscillations, giving rise to an intricate response at the organism level, offering also a potential explanation as to why apparently discordant results were observed in experimental studies. In contrast, high-dose acute ethanol challenge (>8 mM) increases instantaneous CORT levels and the amplitude of ultradian CORT oscillations in a dose-dependent manner, affecting the HPA axis activity also during the following day(s). Chronic exposure to ethanol qualitatively changes the HPA axis dynamics, whereas ethanol at intoxicating levels shuts down this dynamic regulation mechanism. Mathematical modelling gives a quantitative biology-based framework that can be used for predicting how the integral HPA axis response is perturbed by alcohol.

Dynamic transitions in a model of the hypothalamic-pituitary-adrenal axis.

Dynamic properties of a nonlinear five-dimensional stoichiometric model of the hypothalamic-pituitary-adrenal (HPA) axis were systematically investigated. Conditions under which qualitative transitions between dynamic states occur are determined by independently varying the rate constants of all reactions that constitute the model. Bifurcation types were further characterized using continuation algorithms and scale factor methods. Regions of bistability and transitions through supercritical Andronov-Hopf and saddle loop bifurcations were identified. Dynamic state analysis predicts that the HPA axis operates under basal (healthy) physiological conditions close to an Andronov-Hopf bifurcation. Dynamic properties of the stress-control axis have not been characterized experimentally, but modelling suggests that the proximity to a supercritical Andronov-Hopf bifurcation can give the HPA axis both, flexibility to respond to external stimuli and adjust to new conditions and stability, i.e., the capacity to return to the original dynamic state afterwards, which is essential for maintaining homeostasis. The analysis presented here reflects the properties of a low-dimensional model that succinctly describes neurochemical transformations underlying the HPA axis. However, the model accounts correctly for a number of experimentally observed properties of the stress-response axis. We therefore regard that the presented analysis is meaningful, showing how in silico investigations can be used to guide the experimentalists in understanding how the HPA axis activity changes under chronic disease and/or specific pharmacological manipulations.

Modelling cholesterol effects on the dynamics of the hypothalamic-pituitary-adrenal (HPA) axis.

A mathematical model of the hypothalamic-pituitary-adrenal (HPA) axis with cholesterol as a dynamical variable was derived to investigate the effects of cholesterol, the primary precursor of all steroid hormones, on the ultradian and circadian HPA axis activity. To develop the model, the parameter space was systematically examined by stoichiometric network analysis to identify conditions for ultradian oscillations, determine conditions under which dynamic transitions, i.e. bifurcations occur and identify bifurcation types. The bifurcations were further characterized using numerical simulations. Model predictions agree well with empirical findings reported in the literature, indicating that cholesterol levels may critically affect the global dynamics of the HPA axis. The proposed model provides a base for better understanding of experimental observations, it may be used as a tool for designing experiments and offers useful insights into the characteristics of basic dynamic regulatory mechanisms that, when impaired, may lead to the development of some modern-lifestyle-associated diseases.